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What is consumer’s budget constraint?

The initial piece of the utility maximization framework is the consumer's budget constraint. Consumer's budget constraint denotes all possible combinations of goods and services, which a consumer is able to purchase. In other words, consumer's budget constraint denotes the consumption bundle limit, which the consumer can afford. For example, a consumer has to choose among a bundle of goods x1, x2..... xn  , with each good having a price  p1,p2......pn  . Let the income with the consumer as 'I ' to spend for goods. These represent the budget constraints for the consumer. For the case of two goods, say x1, x2  with prices p1,p2. The necessary and sufficient condition for a bundle x1, x2  to be affordable is  p1 x1+ p2x2≤ I. Here budget set denotes the set of affordable bundles. The following figure shows the budget set here.

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The intersecting points of the budget line at  the two axes x1, and x2   are respectively  I/ p1 and I/p2.  The slope of the budget line is p1/p2.Both x1 and x2 ≥ 0 since the consumers can buy only positive amounts of goods. This can be expanded to more than two goods where the budget line is given by p1 x1+ p2x2+...... + pnxn = I.

The following two figures show the effects of price change on the budget line.

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In the first figure, the budget line gets flattened due to the fall in the price of x2.  In the second figure, the budget line gets steepened due to the rise in the price of x2. The next two figures show the effects of change in the income on the budget line.

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The first figure shows that the rise in income results in the flattening of the budget line. The second figure shows a steepening of the budget line due to the fall in the income of the consumer. If the prices of both the goods get doubled, then the equation for the budget line will be  x1 (2p1) + x2(2p2) = I. This means that  x1p1+ x2p2 = I/2. Thus, the effect of doubling the prices of two goods is the same as the effect of cutting the income by half. There can be non-linear budget lines also where the prices are not fixed and variable. The examples include progressive income taxes, volume discounts and food stamps. In all these cases, the budget lines are nonlinear since the prices are not fixed and are changing.

 

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